The guidance method according to the present disclosure reduces aimpoint miss distance sensitivity to mass and motor uncertainties. The guidance method is specifically designed to compensate for solid motors that have the inability to be shut down. This guidance method begins when a velocity-to-go magnitude drops below a threshold that is a function of a specified time constant. Once the guidance method is switched on, a zero effort miss (ZEM) is reduced as though there were a feedback loop nulling the ZEM. At the end of the maneuver the missile attitude will be near the Range Insensitive Axis (RIA) and will continue to hold the ZEM near zero as the motor continues to burn and tail off The method is performed with a novel constraint on the Lambert solution that relies on sensed acceleration feedback rather than any explicit calculation of the ZEM, Instantaneous Impact Point (IIP), or Range Insensitive Axis (RIA), and it can be applied to any ballistic missile that has an exo-atmospheric burnout state. This includes both Earth fixed targets and ballistic intercepts.
PVD guidance is based on the idea that the total ballistic guidance gain is proportional to the missile specific force (sf=thrust/mass) and inversely proportional to the velocity-to-go (Vgo). Dividing sf by Vgo results in units of 1/time which can be thought of as the bandwidth in radians/second. Inverting this equation results in an equivalent first order time constant (Tau=vgo/sf) which is in units of time.
In a typical control feedback loop, a desired time constant is enforced by applying appropriate gain to an error term. For PVD guidance, this error is desired to be the ZEM; however calculating and controlling ZEM directly would require a cumbersome numerical approach. Rather than attempting this, the PVD guidance method of the present disclosure simply constrains Vgo so that Vgo=Tau*sf, through iteration of the Lambert guidance solution which constrains the time-of-flight (TOF). While there is not an explicit ZEM feedback loop, the system behaves as though this loop exists. In fact, the idealized explicit loop may be used in conjunction with the linearized autopilot to predict the linear system response in both the time and frequency domain. This analysis method is referred to herein as the pseudo-loop analogy.
The success of the guidance method has been proven through 6DOF simulation, which demonstrates that the method effectively eliminates any sensitivity to the mass and motor uncertainties that are typically the main guidance accuracy driver when solid boosters are used. Aimpoint dispersions on the order of 100 km due to large motor impulse uncertainty were reduced to less than 5 meters for a 10,000 km trajectory. These results assume perfect navigation, no reentry aerodynamics, and perfect alignment of the thrust vector with the missile axis at zero TVC deflection. The addition of thrust alignment error sources degraded this result to nearly five-hundred meters of miss for 100 Monte-Carlos.